Proverbs 12:22 ESV - Lying lips are an abomination to the Lord, but those who act faithfully are his delight.

Proverbs 11:13 ESV - Whoever goes about slandering reveals secrets, but he who is trustworthy in spirit keeps a thing covered.

Numbers 30:2 ESV - If a man vows a vow to the Lord, or swears an oath to bind himself by a pledge, he shall not break his word. He shall do according to all that proceeds out of his mouth.

Being Trustworthy isn't merely about not telling lies. Gossiping is being untrustworthy toward those around you. A major part of being trustworthy is the commitment to follow through on things you have promised to do.